hard · GMAT Quant

A firm's average cost per unit at production volume x is C(x) = a + b/x, where a and b are positive constants. The firm observes C(20) = 18 and C(30) = 16. A total volume of 60 is split into two unequal positive-integer batches, with x denoting the smaller batch; x is even. A split is acceptable when the two batches' average costs differ by less than 2. The split must remain acceptable after 2 units are moved from the smaller batch to the larger batch.

What is the sum of all possible original values of x?

  1. 48
  2. 50
  3. 52
  4. 54
  5. 78

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